On the structure of the essential spectrum of elliptic operators on metric spaces

Vladimir Georgescu

Published 2010-03-17, updated 2010-04-11Version 2

We give a description of the essential spectrum of a large class of operators on metric measure spaces in terms of their localizations at infinity. These operators are analogues of the elliptic operators on Euclidean spaces and our main result concerns the ideal structure of the $C^*$-algebra generated by them.